Finite Group Databasebeta

← C2×#20245793 #26374573

Subgroups — C2×#20245793 #26374573

Order 12032.

3854 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C212yesmaximal
2C22×C42×D47C211yesmaximal, characteristic
3#20245793C2116yesmaximal, direct product factor
4C2×#15688993C211yesmaximal, characteristic, complemented
5C2×#15688988C212yesmaximal, complemented
6C2×#15688980C214yesmaximal
7C2×C4⋊C4×Dic47C214yesmaximal, complemented
8C2×C47×#384C211yesmaximal, characteristic, complemented
9C23×C4×D47C2212yes—
10C23×C4×D47C2211yescharacteristic
11C2×#13093982—216no—
12C2×#13093982C22116yes—
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2214yes—
15C22×(C2×D47)⋊C4C2214yes—
16C22×C4×Dic47C2214yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C2×C42×D47C4116yescomplemented
20C2×C42×D47C2218yes—
21#15688993C2218yescomplemented
22#15688988C22116yescomplemented
23#15688980C22132yes—
24C4⋊C4×Dic47C22132yescomplemented
25C2×C47⋊#95C2218yes—
26C22×C4⋊C4×C47C2212yes—
27C22×C4⋊C4×C47C2214yes—
28C22×C42×C47C2211yescharacteristic
29C47×#384C2218yescomplemented
30C24×D47C2311yescharacteristic
31C23×Dic47C2314yes—
32C23×Dic47C2312yes—
33C23×Dic47C2311yescharacteristic
34C22×C4×D47—28no—
35C22×C4×D47—28no—
36C22×C4×D47C2×C4116yes—
37C22×C4×D47C2×C418yes—
38C22×C4×D47D418yes—
39C22×C4×D47Q818yes—
40C22×C4×D47C2318yes—
41C22×C4×D47C2314yes—
42#13093982—264no—
43C2×C4⋊Dic47—28no—
44C2×C4⋊Dic47—216no—
45C2×C4⋊Dic47C23116yes—
46C2×C4⋊Dic47C2318yes—
47C2×(C2×D47)⋊C4—216no—
48C2×(C2×D47)⋊C4C23116yes—
49C2×C4×Dic47—216no—
50C2×C4×Dic47C2×C418yes—
51C2×C4×Dic47C2×C4116yes—
52C2×C4×Dic47C23116yes—
53C2×C4×Dic47C2318yes—
54C2×C4×Dic47C2314yes—
55C42×D47C2×C4164yescomplemented
56C47⋊#95C23132yes—
57C23×C4×C47C2314yes—
58C23×C4×C47C2311yescharacteristic
59C23×C4×C47C2312yes—
60C2×C4⋊C4×C47—28no—
61C2×C4⋊C4×C47—216no—
62C2×C4⋊C4×C47C23116yes—
63C2×C4⋊C4×C47C2318yes—
64C2×C42×C47C2×C418yes—
65C2×C42×C47C2314yes—
66C24×C47C2411yescharacteristic
67C23×D47—24no—
68C23×D47—24no—
69C23×D47C22×C414yes—
70C23×D47C2×D414yes—
71C23×D47C2×Q814yes—
72C23×D47C2412yes—
73C22×C4×C47—28no—
74C22×C4×C47—216no—
75C22×C4×C47C22×C414yes—
76C22×C4×C47C22×C418yes—
77C22×C4×C47C2×D414yes—
78C22×C4×C47C2×Q814yes—
79C22×C4×C47#4118yes—
80C22×C4×C47#4118yes—
81C22×C4×C47C2418yes—
82C22×C4×C47C2412yes—
83C22×C4×C47C2414yes—
84C22×Dic47—24no—
85C22×Dic47—24no—
86C22×Dic47—28no—
87C22×Dic47—216no—
88C22×Dic47C22×C418yes—
89C22×Dic47C22×C414yes—
90C22×Dic47C2×D414yes—
91C22×Dic47C2×Q814yes—
92C22×Dic47C2418yes—
93C22×Dic47C2414yes—
94C22×Dic47C2412yes—
95C2×C4×D47—264no—
96C2×C4×D47—216no—
97C2×C4×D47—216no—
98C2×C4×D47C4⋊C4164yescomplemented
99C2×C4×D47C22×C4132yes—
100C2×C4×D47C22×C4116yes—
101C2×C4×D47C2×D4116yes—
102C2×C4×D47C2×Q8116yes—
103C4⋊C4×C47—216no—
104C4⋊C4×C47—232no—
105C42×C47C22×C4116yes—
106(C2×D47)⋊C4—232no—
107C4⋊Dic47—216no—
108C4⋊Dic47—232no—
109C4×Dic47—232no—
110C4×Dic47C22×C4116yes—
111C4×Dic47C22×C4132yes—
112C23×C47C23×C412yes—
113C23×C47C22×D412yes—
114C23×C47C22×Q812yes—
115C23×C47C2×#4114yes—
116C23×C47C2×#4114yes—
117C23×C47C2511yescharacteristic
118C22×D47—216no—
119C22×D47—28no—
120C22×D47—28no—
121C22×D47—216no—
122C22×D47—24no—
123C22×D47—24no—
124C22×D47C2×C4⋊C4116yes—
125C22×D47C23×C414yes—
126C22×D47C22×D414yes—
127C22×D47C22×Q814yes—
128C2×C4×C47—28no—
129C2×C4×C47—216no—
130C2×C4×C47—416no—
131C2×C4×C47C2×C4⋊C4116yes—
132C2×C4×C47#117132yescomplemented
133C2×C4×C47C23×C414yes—
134C2×C4×C47C23×C418yes—
135C2×C4×C47C22×D414yes—
136C2×C4×C47C22×Q814yes—
137C2×C4×C47C2×#4118yes—
138C2×C4×C47C2×#4118yes—
139C2×Dic47—216no—
140C2×Dic47—24no—
141C2×Dic47—24no—
142C2×Dic47—28no—
143C2×Dic47—216no—
144C2×Dic47—416no—
145C2×Dic47C2×C4⋊C4116yes—
146C2×Dic47C23×C418yes—
147C2×Dic47C23×C414yes—
148C2×Dic47C22×D414yes—
149C2×Dic47C22×Q814yes—
150C4×D47—264no—
151C4×D47C2×C4⋊C4164yescomplemented
152C2×#2285—471nomaximal, Sylow
153C22×C47C22×C4⋊C414yes—
154C22×C47C2×#11718yes—
155C22×C47#53214yes—
156C22×C47#53214yes—
157C22×C47#53318yes—
158C22×C47C24×C411yescharacteristic
159C22×C47C23×D411yescharacteristic
160C22×C47C23×Q811yescharacteristic
161C22×C47C22×#4112yes—
162C22×C47C22×#4112yes—
163C2×D47—28no—
164C2×D47—24no—
165C2×D47—24no—
166C2×D47—28no—
167C2×D47—232no—
168C2×D47C22×C4⋊C418yes—
169C4×C47—48no—
170C4×C47C22×C4⋊C418yes—
171C4×C47C2×#117116yescomplemented
172Dic47—28no—
173Dic47—48no—
174Dic47C22×C4⋊C418yes—
175C22×#117—472no—
176C23×C42—471no—
177#2285—4716no—
178C2×#384—471no—
179C2×#384D4711yescharacteristic, complemented
180C2×#382—472no—
181C2×#380—474no—
182C2×C4×C4⋊C4—474no—
183C2×C47#228518yescomplemented
184C2×C47C23×C4⋊C411yescharacteristic
185C2×C47C22×#11712yes—
186C2×C47C2×#53211yescharacteristic
187C2×C47C2×#53211yescharacteristic
188C2×C47C2×#53312yes—
189D47—28no—
190C24×C4—471no—
191C24×C4—472no—
192C2×#117—4716no—
193C2×#117—9416no—
194C22×C4⋊C4—472no—
195C22×C4⋊C4—474no—
196C22×C4⋊C4C2×D4712yes—
197C22×C4⋊C4C2×D4714yes—
198C22×C22⋊C4—474no—
199C22×C42—472no—
200C22×C42—471no—
201C22×C42—4716no—
202C22×C42—478no—
203C22×C42—474no—
204C22×C42C2×D4711yescharacteristic
205#384—478no—
206#384C2×D4718yescomplemented
207#382—4716no—
208#380—4732no—
209C4×C4⋊C4—4732no—
210C2×#95—478no—
211C47C2×#228511yescharacteristic, complemented, Sylow
212C25—471no—
213C23×C4—471no—
214C23×C4—478no—
215C23×C4—478no—
216C23×C4—478no—
217C23×C4—474no—
218C23×C4—472no—
219C23×C4—4716no—
220C23×C4—478no—
221C23×C4—474no—
222C23×C4—948no—
223C23×C4—948no—
224C23×C4C22×D4714yes—
225C23×C4C22×D4711yescharacteristic
226C23×C4C22×D4712yes—
227#117—9464no—
228C2×C4⋊C4—28no—
229C2×C4⋊C4—216no—
230C2×C4⋊C4—478no—
231C2×C4⋊C4—4716no—
232C2×C4⋊C4—948no—
233C2×C4⋊C4—9416no—
234C2×C4⋊C4C22×D4718yes—
235C2×C4⋊C4C22×D47116yes—
236C2×C22⋊C4—4716no—
237C2×C22⋊C4—9416no—
238C2×C42—4716no—
239C2×C42—478no—
240C2×C42—478no—
241C2×C42—474no—
242C2×C42—4764no—
243C2×C42—4716no—
244C2×C42—9416no—
245C2×C42C4×D4718yes—
246C2×C42C22×D4714yes—
247#95—4732no—
248C24—474no—
249C24—474no—
250C24—474no—
251C24—472no—
252C24—944no—
253C24—944no—
254C24C23×D4711yescharacteristic
255C22×C4—28no—
256C22×C4—216no—
257C22×C4—474no—
258C22×C4—474no—
259C22×C4—474no—
260C22×C4—472no—
261C22×C4—4764no—
262C22×C4—4716no—
263C22×C4—4716no—
264C22×C4—4716no—
265C22×C4—478no—
266C22×C4—474no—
267C22×C4—4732no—
268C22×C4—478no—
269C22×C4—944no—
270C22×C4—944no—
271C22×C4—9464no—
272C22×C4—9416no—
273C22×C4—9416no—
274C22×C4—948no—
275C22×C4—9416no—
276C22×C4C2×C4×D4714yes—
277C22×C4C2×C4×D4718yes—
278C22×C4D4×D4714yes—
279C22×C4#1062535218yes—
280C22×C4Q8×D4714yes—
281C22×C4#1062535418yes—
282C22×C4C23×D4718yes—
283C22×C4C23×D4712yes—
284C22×C4C23×D4714yes—
285C4⋊C4—216no—
286C4⋊C4—232no—
287C4⋊C4—9416no—
288C4⋊C4—9432no—
289C22⋊C4—9432no—
290C42—4732no—
291C42—4716no—
292C42—9432no—
293C42C2×C4×D47116yes—
294C23—4716no—
295C23—474no—
296C23—474no—
297C23—474no—
298C23—9416no—
299C23—948no—
300C23—948no—
301C23—9416no—
302C23—944no—
303C23—944no—
304C23C22×C4×D4712yes—
305C23C2×D4×D4712yes—
306C23C2×Q8×D4712yes—
307C23C2×#1062535214yes—
308C23C2×#1062535414yes—
309C23C24×D4711yescharacteristic
310C2×C4—28no—
311C2×C4—216no—
312C2×C4—416no—
313C2×C4—4716no—
314C2×C4—474no—
315C2×C4—474no—
316C2×C4—474no—
317C2×C4—4764no—
318C2×C4—478no—
319C2×C4—9416no—
320C2×C4—944no—
321C2×C4—944no—
322C2×C4—9464no—
323C2×C4—948no—
324C2×C4—9416no—
325C2×C4—18816no—
326C2×C4C4⋊C4×D47116yes—
327C2×C4#13093982132yescomplemented
328C2×C4C22×C4×D4714yes—
329C2×C4C22×C4×D4718yes—
330C2×C4C2×D4×D4714yes—
331C2×C4C2×Q8×D4714yes—
332C2×C4C2×#1062535218yes—
333C2×C4C2×#1062535418yes—
334C22—478no—
335C22—9432no—
336C22—948no—
337C22—944no—
338C22—944no—
339C22—948no—
340C22C2×C4⋊C4×D4714yes—
341C22C2×#1309398218yes—
342C22#1568967114yes—
343C22#1568967414yes—
344C22#1568967818yes—
345C22C23×C4×D4711yescharacteristic
346C22C22×D4×D4711yescharacteristic
347C22C22×Q8×D4711yescharacteristic
348C22C22×#1062535212yes—
349C22C22×#1062535412yes—
350C4—48no—
351C4—478no—
352C4—948no—
353C4—1888no—
354C4C2×C4⋊C4×D4718yes—
355C4C2×#13093982116yescomplemented
356C2—948no—
357C2#2024579318yesdirect product factor
358C2C22×C4⋊C4×D4711yescharacteristic
359C2C22×#1309398212yes—
360C2C2×#1568967111yescharacteristic
361C2C2×#1568967411yescharacteristic
362C2C2×#1568967812yes—
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#384C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#384D47
hypocenterC47C2×#2285
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#384

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #20245793C2direct (N × H)
4. C2×#15688993C2semidirect
5. C2×#15688988C2semidirect
7. C2×C4⋊C4×Dic47C2semidirect
8. C2×C47×#384C2semidirect
19. C2×C42×D47C4semidirect
21. #15688993C22semidirect
22. #15688988C22semidirect
24. C4⋊C4×Dic47C22semidirect
29. C47×#384C22semidirect
55. C42×D47C2×C4semidirect
98. C2×C4×D47C4⋊C4semidirect
132. C2×C4×C47#117semidirect
151. C4×D47C2×C4⋊C4semidirect
171. C4×C47C2×#117semidirect
179. C2×#384D47semidirect
183. C2×C47#2285semidirect
206. #384C2×D47semidirect
211. C47C2×#2285semidirect
327. C2×C4#13093982semidirect
355. C4C2×#13093982semidirect
357. C2#20245793direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130939822
C22×C42×D472
#202457932
C2×#156889932
C2×#156889882
C2×#156889802
C2×C4⋊C4×Dic472
C2×C47×#3842
C2×#228547